Semiconductor/ Semiconductor p-n junctions - UW · PDF file1. semiconductor – metal...

Semiconductor/ Semiconductor

p-n junctions

Dr. Katarzyna Skorupska

Space charge regions in semiconductors

flatband Depletion Inversion Accumulation

1. semiconductor – metal

Schottky contact

2. semiconductor – semiconductor

p-n junction

homojunction (p-Si : n-Si) , heterojunction

3. semiconductor - electrolyte

Schottky like contact

Space charge layer

Leads to spatial separation of charges minority carriers are driven to the surface by

electric field

Field acceleration impacts excess energy to both carriers

semiconductor – semiconductor

p-n junction

homojunction (p-Si : n-Si) , heterojunction

Contact potentials and space charge layers

With the Ansatz that the charge is distributed evenly with x (homogenous doping) one considers the relation of :

charge,

electric field,

electrostatic potential

and energy:

Poisson´s equation connects charge and potential:

Here, since d 0, which holds for homojunctions, we have set Y and continue to use the latter from now on.

+ + + + + +

donors

acceptors

neutral neutral -Wp

p-type n-type

– Galvani potential

y– Volta potential (electrostatic)

d – surface dipole changes

– charge density

Δ – LaPlace operator

+ + + + + +

donors

acceptors

neutral neutral -Wp

p-type

pAqN 0 xWp

nDqN nWx 0

n-type

Wn,p - spatial limit of charged areas

First integration of φ with respect to x

dx2= -

rnene0

= -qND

, r = -qNDd2j

dx2= -

= -(-qNA )

, rp = qNA

with E’ as electric field:

The first integral yields the electric field since E’= -grad φ

p-type n-type

dx=qNA

dx= -qNA

E '(x) = -qNA

x +C '

for -Wp £ x £ 0

dx= -qND

dx=qND

E '(x) =qND

for 0 £ x £Wn

-Wp Wn

for x = 0

E '(x) = -qNA

x +C '

E '(x) =C '

forx = 0

E '(x) =qND

E '(x) =C

-Wp Wn

p-type n-type

For x=0 the electric field attains its maximum value.

p-type n-type

xEWxfor

-Wp Wn

The integration constant is determined by the boundary condition that E’(x) vanishes outside the charged region

p-type n-type

-Wp Wn

Electric field is given by

Graphic integration for semiconductor pair

E '(x) =qND

x -Wn( )E '(x) = -qNA

x+Wp( )

p-type n-type

For x=0 the electric field attains its maximum value.

nnnppp

WqNWqN

xsufracetheatntdisplacemedielectricD

)0()0(

)0(')0('

)0(')0()0(')0(

Extension of space charge layer is inversely proportional to the respective doping layer.

higher relative doping –smaller the space charge layer

p-type n-type

second derivative to know φ (electrostatic potential)

dxWxqN

p-type n-type

at the surface (x=0) Galvani potential is equal zero (φ=0)

The energetic position of the band edges at the surface of each material remains unaltered.

Graphic integration for semiconductor pair

D WxqN

A WxqN

p-type n-type

1()( 2

E = ej = -qj

electric field

galvani potential

energy

Graphic integration for semiconductor pn junctions

Junction geometry and charge distribution (which material has a higher doping concentration?)

The charge profile

The electrical field across the contact (E = - d/dx)

Second integration: Galvani or electrostatic

potential

Energy E = e = -q sign change

p-type n-type

diffusion potential defined by the electric potential difference

Vp = f(0)-f(-Wp )

fp(x) =qNA

2x2 +Wpx

Vp =qNA

(0 + 0)-qNA

2 + (Wp × (-Wp )æ

Vp = -qNA

Vp = -Wp

Vp = - -1

ø÷Wp

Vp =qNAWp

Vn = f(Wn )-f(0)

fn (x) = -qND

2x2 -Wnx

Vn = -qND

2 - (Wn ×Wn )æ

ø÷- -

(0 + 0)æ

èçç

ø÷÷

Vn = -qND

Vn = -Wn

Vn = - -1

ø÷Wn

Vn =qNDWn

Nbecause

p-type n-type

qNWqNV

Graphic integration for semiconductor pn junctions

Important relations for pn junctions

(to memorize)

nDpA WNWN

Electroneutrality condition

Diffusion voltage relations

The width of the space charge layer depends on:

• doping level

• voltage drop

Eg=1.12 eV

NCB=3.2 1019 cm-3

ND=1017 cm-3

Eg=1.12 eV

NVB=1.8 1019 cm-3

NA=1015 cm-3

p-type n-type

kT=26 meV

n-type p-type

Position of nEF before contact Position of pEF before contact

EF = EVB - kT lnNVB

NAEF = ECB - kT ln

EF -EVB = kT lnNVB

NAECB -EF = kT lnNCB

ECB -EF = 26 ln3.2 ×1019

1017meV

ECB -EF = 26 ln3.2 ×102

ECB -EF = 26 ×5.7

ECB -EF =150meV

ECB -EF = 0.15meV

EF -EVB = 26 ln1.8 ×1019

1015meV

EF -EVB = 26 ln1.8 ×104

EF -EVB = 26 ×9.8

EF -EVB = 254.8meV

EF -EVB = 0.25meV

ECB ECB

EVB EVB

F 0.25 eV

0.15 eV

Contact potential difference

ECB ECB

EVB EVB

F 0.25 eV

0.15 eV

eVC = nEF - pEF = eVn -eVp = e(Vn -Vp ) =

= Eg - (nEF + pEF ) =1.12 - (0.15+ 0.26) = 0.71eV

Changes of position of nEF and pEF after contact formation

pEF® eVpnEF® eVn eVc = nEF - pEF = eVn + eVp

1017=10-2 = 0.01

Vn =NA

Vn = aVp

VC =Vn +Vp

VC = aVp +Vp =Vp(a +1)

Vp =VC

(a +1)

Vn =VC -Vp

Vn = 0.71- 0.703 = 0.007

Vp =VC

(a +1)

Vp =0.71

0.01+1= 0.703

Wn =2e0enVnqND

en =11.7

ND =1017cm-3

Vn = 0.007eV

Wp =2e0e pVp

e p =11.7

NA =1015cm-3

Vp = 0.703eV

Wn =2 ×8.85 ×10-14 ×11.7 ×0.007

1.6 ×10-19 ×1017

Wn =1.45 ×10-14

1.6 ×10-2

Wn = 0.9 ×10-12

Wn = 9.5 ×10-7

Wp =2 ×8.85 ×10-14 ×11.7 ×0.703

1.6 ×10-19 ×1015

Wp =145 ×10-14

1.6 ×10-4

Wp = 90.6 ×10-10

Wp = 9.5 ×10-5

e0 = 8.85 ×10-14[Fcm

q =1.6 ×10-19[C]

cm=A × s

V ×cm

ND[cm-3]

q[C = A × s]

A × s

V ×cmV

A × s ×cm-3=A × s

cmA × s ×cm-3 = cm

Current voltage characteristic at p-n junction

For simplicity we consider:

- homojunction

- electron current

- voltage dependence of n-type side of the junctions

Absence of generation and recombination of carriers within the space charge layer

Electron current (from n-type to p-type) jnr

– number of e- on the n-type side that can thermally overcome the barrier given by

energetic distance between ECBn and ECB

Majority carriers (e-) on the n-type side become minority carriers on the p-type side

where they recombine.

Electron current (from p-type to n-type) jng

- thermal generation of e- in the neutral region of the p-type junction

- Drift to the n-type side

- Minority carriers (e-) on the p-type side become majority carriers on the n-type

r – recombination

g - generation

The recombination current jnr from n-type to p-type at the equilibrium:

-by contact potential difference Vd

jnr (Va = 0) = jnr (Vd ) = en thn(Vd ) = en thn0eeVd

Va – applied potential

Vd – potential difference

vth - thermal velocity

n(Vd)- carrier concentration

n0 – concentration of e- at the bottom of conduction band (given by doping level)

Thermal excitation of e- at the p-type side

in the EVB across the Eg

jng = qn thNVBeEg

kT = qn thnp

np – e- concentration in the neutral region of ECB of p-type sc

eVd +ECB -EFC << Eg

jnr ¹ jng

Applying negative voltage (forward) to the n-type side:

- decrease of band bending

- jnr increase

- jng is not influenced

jnr (Va ) = en thn0e

e Vd-Va( )kT = jnr (0)e

Va – applied potential

Vd – potential difference

vth - thermal velocity

n(Vd)- carrier concentration

n0 – concentration of e- at the bottom of conduction band (given by doping level)

jnr (0) = en thn0eeVd

Applying positive voltage (reverse) to the n-type side:

- increase of band bending

- Jnr decrease exponentially with the increase barrier height

- jng is not influenced

jnr (Va ) = en thn0e-e Vd+Va( )kT = jnr (0)e

kT jnr (0) = en thn0eeVd

jng(Va ) = jnr (0) = j0eeVd

jn(Va ) = j0eeVd

kT eeVa

kT -1æ

ø÷ = jng e

kT -1æ

jD(Va ) = jn(Va )+ jp(Va )Total current:

Total e- dark current: sum of generation and recombination currents (opposite sign)

jn(Va ) = jnr (Va )- jng(Va )

jnr (Va ) = en thn0e-e Vd+Va( )kT = jnr (0)e

using:

jng(Va ) = jng(0) = - jnr (0)

jD = jng + jpg( ) eeV

kT -1æ

Diode relationship by Shockley

jD = js eeV

kT -1æ

js – reverse saturation current described by

metal glow emission properties jng+ jpg – diffusion constants and minority

carrier diffusion lengths

js = jng + jpg =eDpp0

Lp+eDnn0

Constant illumination- number of absorbed photons per second and cm2 mulitiled by

elementary charge

Light induced photocurrent: jL = enph(Eg )(1-R)

- p-type – photoactive part

- positive dark current under forward bias

from p-type absorber to n-type emitter

- photocurrent is opposite sign

- photocurrent does not exhibit voltage

dependent (simple approach)

Where:

jPh- photocurrent

jD- dark current

Js- dark saturation current

jL- light-induced current

nPh- number of absorbed photons per second and

R- sample reflectivity

Photocurrent – dark- and light induced current (having opposite sign)

jph = jD - jL = js eeV

kT -1æ

ø÷- jL

- p-type – photoactive part

- positive dark current under forward bias

from p-type absorber to n-type emitter

- photocurrent is opposite sign

- photocurrent does not exhibit voltage

dependent (simple approach)

Where:

jPh- photocurrent

jD- dark current

Photocurrent

The approximation for the light induced current (jL)

jph = jD - jL = js eeV

kT -1æ

ø÷- jL

Photocurrent dependence follows dark-current-voltage behavior

)1()( REhenj gPhL

Where:

jPh- photocurrent

jD- dark current

Short circuit current jL (Rext ~ 0)

Open circuit voltage VOC (R ∞)

Maximum power point MPP (largest area under jPh curve)

Current and voltage at Maximum power point jMP , VMP

Output power Pout = jMP x VMP

Solar Cell efficiency h = Pout / Pin , Pin : light intensity

Semiconductor/Metal Schottky type junctions

Dr. Katarzyna Skorupska

4.05 eV

0.2-0.3 eV

1.12 eVEg

ECB-energy of conduction band lowest unoccupied level EVB- energy of valence band highest occupied level Eg- band gap energy distance between EVB and ECB EF- Fermi level

Work function -is the minimum energy (usually measured in electronvolts) needed to remove an electron from a solid to a point immediately outside the solid surface (or energy needed to move an electron from the Fermi level into vacuum). Electron affinity - is the energy difference between the vacuum energy and the conduction band minimum

semiconductor – metal Schottky contact

Thermionic interaction - Contact formation based on energetic considerations - Interfacial effects neglected

semiconductor metal

mobile nature of charges

under contact formation development of electrical field Potential drop across interface

EFsc EF

redistribution of charges on the metal side

Metal - semiconductor Schottky contact (rectifying semiconductor-metal junction)

Definition: contact potential difference

∆Εc = EFSC – EF

M = ΦM - ΦSC

The junction is characterized by • the semiconductor and metal

work function (ΦSC- given by doping) • the semiconductor electron

affinity and its energy gap.

Contact formation (ideal case: absence of surface states) Consider a neutral but doped (n-type) semiconductor and a metal with higher work function before contact:

Schottky junction formation

Consider a n-type semiconductor-metal contact where the work function of the metal is higher: a macroscopic gap between the phases decreases successively until contact;

connected by a conductive wire : equilibrium formation

Metal (high e- concentration -> electrostatic field at top most layer (0.1Å) - the potential drop can be neglected

Electrostatic effects are restricted to the SC side

contact energy difference eVc drops exclusively across the interlayer gap d (the vacuum level course)

Schottky junction formation cont´d Definitions: barrier height and band bending; relation between them:

Barrier height defines in Schottky (photo)diodes the reverse saturation current as will be shown below.

Lowered distance d - lowered energetic drop across the interlayer eVc

(1) - Partial contact energy difference in the SC eVc

Distance d=0 - difference in EF

M and EFSC drops completely in the SC space

charge region

Barrier height – energetic barrier e- have to overcome to enter the other phase. ΦBh- energetic distance between EF

M (after contact formation EF

M=EFSC) and the band edge ECB

ΦBh = eVbb + ECB - EF

Short circuiting semiconductor and metal and decreasing their distance: • electrons flow from the semiconductor to the metal the metal becomes negatively charged,

the semiconductor positively

• at small, finite distance, the contact potential VC drops across the air gap and the

semiconductor surface region

• the relative distribution of VC follows where CM and CSC denote metal and semiconductor capacitance, respectively

Schottky Junctions

The electron depletion of the semiconductor during contact formation leads to a charged region near the surface;

Schottky barrier: Decreasing the gap to zero:

Origin of the spatial dependence of the energy bands and the vacuum level: Poisson´s equ. in 1dimension

• the contact potential drops almost exclusively across the semiconductor near surface region

(depending on doping and contact potential difference, i.e. extension of the charged region). • BARRIER HEIGHT (Φbh): energetic

barrier which metal electrons have to overcome (thermally) to reach the semiconductor.

• Band banding (eVbb)

C - capacitance; Q - charges on the plates; V - the voltage between the plates; A - area of overlap of the two plates; εr - relative static permittivity (sometimes called the dielectric constant) of the material between the plates (for a vacuum, εr = 1); ε0 - electric constant (ε0 ≈ 8.854×10−12 F m–1); d - separation between the plates.

Space charge regions in semiconductors

flatband Depletion

Space charge regions in semiconductors II

Inversion

Space charge regions in semiconductors III

Inversion Accumulation

forward current – from n-SC to metal reverse current – from metal to n-SC

Dark current – influence of applied voltage to determine electron currents from: • semiconductor to metal (forward current) • metal to semiconductor (reverse current) to find the expressions for the currents based on the thermionic emission model for an applied voltage (forward and reverse currents)

n-semiconductor

interface barrier

The thermionic emission model

(i) the barrier height is much larger than the thermal energy (Φbh >>kT),

(ii) thermal equilibrium exists in the plane of emission (x =0) and (i) non-degenerate semiconductors

• the band edge positions at the surface (x=0) remain unaltered hence the barrier height does not change

• the (cathodic) voltage reduces the band bending • the Fermi levels on both sides of the junction are different

The dark current from semiconductor is given:

16 νth- thermal velocity

Expression for the forward current (SC to M)

using the Boltzmann exponential term

The voltage dependence of the current density is given by the energetic shift of the Fermi level EF(0) to EF(V) using EF(V) = EF(0) + eVc one obtains for the (increased) carrier concentration at the semiconductor surface:

the forward current is given:

The expression ECB-EF(0) represents the barrier height of the junction (Φbh). The forward dark current density can then be expressed in terms of the barrier height and applied voltage:

The expression of the thermal velocity (vth) and the effective density of states (DOS) at the conduction band edge (ECB) by their dependence on temperature and effective electron mass (m*

thermal velocity effective DOS

using the expression for the effective Richardson constant which describes the glow-emission properties of a material

one obtains the equation for the dark current in forward direction

Current from metal to semiconductor (reverse current)

In the equilibrium situation considered for V=0 The forward current (SCM) must be equal and opposite in sign to the reverse current (MSC) Therefore:

To ta l c u r r e nt

The pre-factor called reverse saturation current (js) • contains material properties • temperature • and gives the current at V=0

eTAjΦ

−= 2*

DIODE CHARACTERISATION

question: which sign for voltage and current for an n-type semiconductor-metal junction?

Photocurrent

The approximation for the light induced current (jL)

Photocurrent dependence follows dark-current-voltage behavior

)1()( REhenj gPhL −⋅>= ν

Where: jPh- photocurrent jD- dark current Js- dark saturation current jL- light-induced current nPh- number of absorbed photons per second and cm2 R- sample reflectivity Short circuit current jL (Rext ~ 0)

Open circuit voltage VOC (R ∞)

Maximum power point MPP (largest area under jPh curve)

Current and voltage at Maximum power point jMP , VMP

Output power Pout = jMP x VMP

Solar Cell efficiency η = Pout / Pin , Pin : light intensity

Illumination of the semiconductor with photons of energy greater than Eg, - accumulates the electrons in semiconductor side and - holes in the metal side of the depletion region. There occurs an electron-hole pair generation. The light splits the Fermi level and creates a photovoltage V, equal to the difference in the Fermi levels of semiconductor and metal far from the junction.

At open-circuit voltage (VOC) the photocurrent is equal zero IPh=0

Photovoltage (Vph) is given by jph=0

+== 1ln

LOCPh j

the photovoltage changes logarithmically with the light intensity

VPh = 0.74V

+== 1ln

LOCPh j

Example:

Semiconductor/ Semiconductor p-n junctions - UW · PDF file1. semiconductor – metal...

Documents

Transcript of Semiconductor/ Semiconductor p-n junctions - UW · PDF file1. semiconductor – metal...

ELCT 563 – Semiconductor Electronic Devices Introduction.pdf · to solve problems on basic semiconductor material properties, principles and characteristics of semiconductor p-n

Record High Eﬃciency Single-Walled Carbon Nanotube/Silicon ... · 9/24/2012 · suggests that these hybrid solar cells operate in the same manner as single crystalline p−n homojunction

Fun Electron Tricks Semiconductor Devices npn junction Put another n-type semiconductor on the other side of the p-type semiconductor No matter which.

Core-shell homojunction silicon vertical nanowire … Core-shell homojunction silicon vertical nanowire tunneling field-effect transistors Jun-Sik Yoon 1, Kihyun Kim1, and Chang-Ki

2 1 Cooling p m p of Power Switching Semiconductor Devices

Solution-processed oxide semiconductor SnO in p-channel …S1 Electronic Supplementary Information (ESI) Solution-processed oxide semiconductor SnO in p-channel thin-film transistors

Endra dwi p i8110019 semiconductor manufacture

Semiconductor Physics Part 2...semiconductor, such as a classical silicon PN junction, is called a homojunction. Slide 11/17 Wei SHA 1. P-N heterojunction (2) Band-diagram cp n cvGNgp

Semiconductor Devices 25 - University of York€¦ · 25 Metal Semiconductor Junction • Work function • Metal / n-type semiconductor • Metal / p-type semiconductor • Einstein

一般而言， p-n 接面可分為同質接面 (Homojunction) 與 異質接面 (Heterojunction) 。

STRAINED-LAYER InGaAs(P) QUANTUM WELL SEMICONDUCTOR … Bound... · SEMICONDUCTOR LASERS AND SEMICONDUCTOR ... quantum well semiconductor lasers and amplifiers for applications in

PLC I/O Semiconductor devices I/O modules. Semiconductor components Semiconductor devices are made of p-type and n-type materials. A device with one p-type.

Lecture 19: Semiconductor Devices Kittel Ch. 17, p. 503 ...

Soft Semiconductor Devices - RLE at MIT · Soft Semiconductor Devices 11-1 Soft Semiconductor Devices Academic and Research Staff ... Project Staff C. L. Mulder, P. D. Reusswig, A.

Radiofrequency Plasma Sources for Semiconductor …ffchen/Publs/Chen213P.pdf · 6 6 Radiofrequency Plasma Sources for Semiconductor Processing. 6-6. p / / is ...

Metal-semiconductor-metal photodetectors based on …poplab.stanford.edu/pdfs/AnBehnam-MSMgrapheneSi-apl13.pdf · Metal-semiconductor-metal photodetectors based on graphene/p ...

Franchised Product Line Card - chip1.com · • indie semiconductor • ISC Semiconductor • Isocom P • Para Light • Patriot Memory • Pilkor • Prema Semiconductor • Pretec

Compound Semiconductor - Institute of Physicsdownload.iop.org/cs/cs_14_03.pdf · Compound Semiconductor month 2008 Volume 14 number X ConneCting the Co m p o u n d SemiConduCtor Co

40V P-Channel MOSFETs PDC4903ZPotens semiconductor corp. Ver.1.01

PN JUNCTION THEORY - Polytech Nice Sophia ...users.polytech.unice.fr/~lorenz/PN_junction_eng.pdfPN Homojunction • Non linear device • rectifier devices (composants redresseur)

一般而言， p-n 接面可分為同質接面 (Homojunction) 與異質接面 (Heterojunction) 。